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Question

At 40C, a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod when it is heated to 240C? The coefficients of linear expansion of brass and steel are 2.0×105 C1 and 1.2×105 C1 respectively.


A

0.28 cm

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B

0.30 cm

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C

0.32 cm

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D

0.34 cm

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Solution

The correct option is C

0.32 cm


The increase in the length of the brass rod, Δlb=2×105×0.5×(24040)=0.2 cm
The increase in the length of the steel rod, Δls=1.2×105×0.5×(24040)=0.12 cm
Increase in the length of the composite rod, Δl=Δlb+Δls=0.20+0.12=0.32 cm
Hence, the correct choice is (c).


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